What is the inverse of f(x)=(e^{x-5}+3)/2 ?

The inverse of f(x)=(e^{x-5}+3)/2 is ln(x*2-3)+5

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inverse of f(x)=(e^{x-5}+3)/2

inverse

f (x) = \frac{e ^{x - 5} + 3}{2}

ln (x \cdot 2 - 3) + 5

Solution steps

y = \frac{e ^{x - 5} + 3}{2}

Replace

x

with

y

x = \frac{e ^{y - 5} + 3}{2}

Solve for

y, x = \frac{e ^{y - 5} + 3}{2}

ln (x \cdot 2 - 3) + 5

y = 4 x + 3

f (x) = x^{2} - x - 2

f (x) = \frac{6 x - 1}{x + 4}

f (x) = 1 + 6 + 7 x

\frac{( x - 1 ) ^{2}}{81}

What is the inverse of f(x)=(e^{x-5}+3)/2 ?
The inverse of f(x)=(e^{x-5}+3)/2 is ln(x*2-3)+5